Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of 264)

Label	Polynomial	Discriminant	Galois group	Class group
16.4.165855107822265625.1	x^16 - 2x^15 + x^14 - 3x^12 + 5x^11 - 8x^10 + 34x^9 - 24x^8 - 31x^7 + 32x^5 + 15x^4 - 16x^3 - 8x^2 + 2x + 1	\( 5^{10}\cdot 19^{8} \)	$C_2^4.D_4$ (as 16T339)	Trivial
16.0.165855107822265625.1	x^16 - 7x^14 + 21x^12 - 32x^10 + 20x^8 + 2x^6 + 16x^4 + 7x^2 + 1	\( 5^{10}\cdot 19^{8} \)	$C_2^4.D_4$ (as 16T339)	Trivial
16.4.1103097268369140625.1	x^16 - 4x^15 + 6x^14 - 2x^13 - 15x^12 + 26x^11 - 33x^9 + 33x^8 + 6x^7 - 47x^6 + 12x^5 + 26x^4 - 17x^3 - 17x^2 - x + 1	\( 5^{10}\cdot 7^{4}\cdot 19^{6} \)	$C_2^4.D_4$ (as 16T339)	Trivial
16.0.2113922820157210624.3	x^16 + 6x^14 + 12x^12 + 11x^10 + 17x^8 + 8x^6 + 12x^4 - 4x^2 + 4	\( 2^{20}\cdot 17^{10} \)	$C_2^4.D_4$ (as 16T339)	Trivial
16.0.10366407720712890625.1	x^16 + 7x^14 + 16x^12 + 17x^10 + 19x^8 + 17x^6 + 16x^4 + 7x^2 + 1	\( 5^{10}\cdot 101^{6} \)	$C_2^4.D_4$ (as 16T339)	Trivial
16.0.10366407720712890625.2	x^16 - 4x^15 + 12x^14 - 22x^13 + 41x^12 - 66x^11 + 122x^10 - 181x^9 + 255x^8 - 276x^7 + 265x^6 - 192x^5 + 94x^4 - 15x^3 - 25x^2 + 15x + 5	\( 5^{10}\cdot 101^{6} \)	$C_2^4.D_4$ (as 16T339)	Trivial
16.0.31549122067433507289.1	x^16 - 3x^15 + 2x^14 - 4x^13 + 10x^12 - 10x^11 + 78x^10 - 264x^9 + 462x^8 - 572x^7 + 594x^6 - 532x^5 + 392x^4 - 224x^3 + 92x^2 - 24x + 3	\( 3^{8}\cdot 37^{10} \)	$C_2^4.D_4$ (as 16T339)	Trivial
16.4.31549122067433507289.1	x^16 - 7x^15 + 13x^14 + 9x^13 - 41x^12 - 7x^11 + 77x^10 + 5x^9 - 109x^8 + 5x^7 + 77x^6 - 7x^5 - 41x^4 + 9x^3 + 13x^2 - 7x + 1	\( 3^{8}\cdot 37^{10} \)	$C_2^4.D_4$ (as 16T339)	Trivial
16.4.59873693923837890625.1	x^16 - x^15 - 5x^14 + 5x^13 + x^12 - 35x^11 - 25x^10 + 157x^9 + 34x^8 - 306x^7 + 83x^6 + 316x^5 - 109x^4 - 235x^3 + 20x^2 + 75x + 25	\( 5^{10}\cdot 19^{10} \)	$C_2^4.D_4$ (as 16T339)	Trivial (GRH)
16.0.59873693923837890625.3	x^16 + 11x^14 + 54x^12 + 184x^10 + 429x^8 + 736x^6 + 864x^4 + 704x^2 + 256	\( 5^{10}\cdot 19^{10} \)	$C_2^4.D_4$ (as 16T339)	$[2]$
16.4.73786976294838206464.4	x^16 - 4x^12 - 48x^10 + 130x^8 - 224x^6 + 132x^4 - 16x^2 + 1	\( 2^{66} \)	$C_2^4.D_4$ (as 16T339)	Trivial (GRH)
16.0.73786976294838206464.6	x^16 - 4x^12 + 48x^10 + 130x^8 + 224x^6 + 132x^4 + 16x^2 + 1	\( 2^{66} \)	$C_2^4.D_4$ (as 16T339)	Trivial
16.4.73786976294838206464.12	x^16 - 4x^12 + 18x^8 - 64x^6 - 220x^4 - 192x^2 + 49	\( 2^{66} \)	$C_2^4.D_4$ (as 16T339)	Trivial (GRH)
16.0.73786976294838206464.12	x^16 - 4x^12 + 18x^8 + 64x^6 - 220x^4 + 192x^2 + 49	\( 2^{66} \)	$C_2^4.D_4$ (as 16T339)	Trivial
16.4.283942098606901565601.1	x^16 - 4x^15 + 2x^14 + 12x^13 - 28x^12 + 10x^11 + 43x^10 - 36x^9 - 77x^8 + 36x^7 + 43x^6 - 10x^5 - 28x^4 - 12x^3 + 2x^2 + 4x + 1	\( 3^{10}\cdot 37^{10} \)	$C_2^4.D_4$ (as 16T339)	Trivial (GRH)
16.0.283942098606901565601.3	x^16 - 5x^15 + 3x^14 + 20x^13 - 17x^12 - 61x^11 + 40x^10 + 146x^9 - 56x^8 - 220x^7 - 2x^6 + 218x^5 + 63x^4 - 104x^3 - 44x^2 - 6x + 33	\( 3^{10}\cdot 37^{10} \)	$C_2^4.D_4$ (as 16T339)	$[2]$
16.0.1433890992229697265625.1	x^16 - 2x^15 + 6x^14 - 3x^13 + 3x^12 + 36x^11 - 7x^10 + 46x^9 + 61x^8 - 121x^7 + 33x^6 + 38x^5 - 132x^4 + 213x^3 + 35x^2 - 207x + 99	\( 5^{10}\cdot 59^{8} \)	$C_2^4.D_4$ (as 16T339)	Trivial
16.4.1433890992229697265625.1	x^16 + 13x^14 + 21x^12 - 52x^10 - 80x^8 + 82x^6 + 36x^4 - 33x^2 + 1	\( 5^{10}\cdot 59^{8} \)	$C_2^4.D_4$ (as 16T339)	Trivial (GRH)
16.0.3055545398040538937521.1	x^16 - 7x^15 + 30x^14 - 93x^13 + 216x^12 - 397x^11 + 591x^10 - 736x^9 + 834x^8 - 900x^7 + 925x^6 - 775x^5 + 487x^4 - 261x^3 + 118x^2 - 33x + 9	\( 13^{10}\cdot 53^{6} \)	$C_2^4.D_4$ (as 16T339)	Trivial
16.0.3055545398040538937521.2	x^16 - x^15 + 6x^14 - 18x^13 + 31x^12 - 65x^11 + 182x^10 - 222x^9 + 488x^8 - 865x^7 + 892x^6 - 1185x^5 + 1412x^4 - 189x^3 + 716x^2 - 45x + 81	\( 13^{10}\cdot 53^{6} \)	$C_2^4.D_4$ (as 16T339)	Trivial
16.4.4680242843420172745161.1	x^16 - 4x^15 - 4x^14 + 40x^13 - 32x^12 - 144x^11 + 251x^10 + 244x^9 - 878x^8 + 178x^7 + 1599x^6 - 2072x^5 + 679x^4 + 546x^3 - 578x^2 + 200x - 25	\( 3^{8}\cdot 61^{10} \)	$C_2^4.D_4$ (as 16T339)	Trivial
16.0.4680242843420172745161.1	x^16 - 4x^15 + 13x^14 - 33x^13 + 73x^12 - 191x^11 + 470x^10 - 1047x^9 + 1981x^8 - 3106x^7 + 4246x^6 - 4978x^5 + 5090x^4 - 4431x^3 + 2977x^2 - 1395x + 339	\( 3^{8}\cdot 61^{10} \)	$C_2^4.D_4$ (as 16T339)	Trivial
16.0.7102521108903347083489.1	x^16 - x^15 + 13x^14 - 3x^13 + 40x^12 + 40x^11 + 42x^10 + 132x^9 + 77x^8 + 4x^7 + 144x^6 + 2x^5 - 230x^4 - 78x^3 + 117x^2 + 78x + 13	\( 13^{10}\cdot 61^{6} \)	$C_2^4.D_4$ (as 16T339)	Trivial (GRH)
16.0.7102521108903347083489.2	x^16 - 6x^15 + 17x^14 - 43x^13 + 93x^12 - 97x^11 + 210x^10 - 126x^9 + 372x^8 - 211x^7 + 474x^6 - 263x^5 + 359x^4 - 186x^3 + 137x^2 - 55x + 25	\( 13^{10}\cdot 61^{6} \)	$C_2^4.D_4$ (as 16T339)	Trivial (GRH)
16.0.10795834326047897474569.1	x^16 - 5x^15 + 21x^14 - 51x^13 + 122x^12 - 204x^11 + 380x^10 - 515x^9 + 781x^8 - 759x^7 + 816x^6 - 430x^5 + 321x^4 - 62x^3 + 116x^2 - 24x + 16	\( 13^{10}\cdot 23^{8} \)	$C_2^4.D_4$ (as 16T339)	Trivial
16.4.10795834326047897474569.1	x^16 - 2x^15 - 9x^14 + 31x^13 + 15x^12 - 156x^11 + 96x^10 + 404x^9 - 533x^8 - 353x^7 + 559x^6 + 270x^5 - 187x^4 - 292x^3 + 72x + 16	\( 13^{10}\cdot 23^{8} \)	$C_2^4.D_4$ (as 16T339)	Trivial (GRH)
16.0.14815515721743759765625.1	x^16 - x^15 + 5x^14 + 6x^13 - 9x^12 - 81x^11 + 65x^10 + 241x^9 - 150x^8 - 234x^7 + 440x^6 + 109x^5 - 14x^4 - 44x^3 + 65x^2 + 4x + 1	\( 5^{10}\cdot 79^{8} \)	$C_2^4.D_4$ (as 16T339)	Trivial (GRH)
16.4.14815515721743759765625.1	x^16 - 7x^15 + 16x^14 - 21x^13 + 33x^12 + 11x^11 - 166x^10 + 388x^9 - 892x^8 + 1476x^7 - 1297x^6 + 1240x^5 - 2443x^4 + 2770x^3 - 1012x^2 - 352x + 256	\( 5^{10}\cdot 79^{8} \)	$C_2^4.D_4$ (as 16T339)	Trivial (GRH)
16.0.21730832354890360782721.1	x^16 - 7x^14 - 11x^12 + 66x^10 + 178x^8 + 490x^6 + 1069x^4 + 837x^2 + 81	\( 17^{10}\cdot 47^{6} \)	$C_2^4.D_4$ (as 16T339)	Trivial (GRH)
16.0.21730832354890360782721.2	x^16 - 2x^15 + 4x^14 + 5x^13 + x^12 + 16x^11 + 73x^10 + 23x^9 + 252x^8 + 351x^7 - 445x^6 - 690x^5 + x^4 - 55x^3 + 76x^2 + 288x + 117	\( 17^{10}\cdot 47^{6} \)	$C_2^4.D_4$ (as 16T339)	Trivial (GRH)
16.8.35767658757222150701056.1	x^16 - 6x^15 + 7x^14 + 6x^13 - 2x^12 - 34x^11 - 67x^10 + 194x^9 + 138x^8 - 194x^7 - 67x^6 + 34x^5 - 2x^4 - 6x^3 + 7x^2 + 6x + 1	\( 2^{34}\cdot 113^{6} \)	$C_2^4.D_4$ (as 16T339)	Trivial (GRH)
16.8.35767658757222150701056.2	x^16 - 4x^15 - 10x^14 + 52x^13 + 26x^12 - 248x^11 + 34x^10 + 496x^9 - 288x^8 - 204x^7 + 712x^6 - 584x^5 - 1337x^4 + 500x^3 + 1810x^2 + 112x - 1084	\( 2^{34}\cdot 113^{6} \)	$C_2^4.D_4$ (as 16T339)	Trivial (GRH)
16.4.42122185590781554706449.1	x^16 - 3x^15 - 2x^14 + 11x^13 - 11x^12 + x^11 + 38x^10 - 73x^9 + 24x^8 + 122x^7 - 131x^6 - 5x^5 + 46x^4 + 37x^3 - 336x^2 + 427x - 137	\( 3^{10}\cdot 61^{10} \)	$C_2^4.D_4$ (as 16T339)	Trivial (GRH)
16.0.42122185590781554706449.3	x^16 - x^15 - 11x^14 - x^13 + 55x^12 + 43x^11 - 135x^10 - 125x^9 + 251x^8 + 53x^7 - 666x^6 + 284x^5 + 2486x^4 + 1953x^3 - 665x^2 - 750x + 375	\( 3^{10}\cdot 61^{10} \)	$C_2^4.D_4$ (as 16T339)	$[2]$ (GRH)
16.8.68014001055597275390625.1	x^16 - 4x^15 - 18x^14 + 78x^13 + 118x^12 - 532x^11 - 517x^10 + 1774x^9 + 1721x^8 - 2944x^7 - 3319x^6 + 2066x^5 + 2613x^4 - 1348x^3 - 1613x^2 + 604x + 619	\( 3^{8}\cdot 5^{10}\cdot 101^{6} \)	$C_2^4.D_4$ (as 16T339)	Trivial (GRH)
16.8.68014001055597275390625.2	x^16 - 23x^14 + 235x^12 - 1365x^10 + 4810x^8 - 10123x^6 + 11469x^4 - 5130x^2 + 25	\( 3^{8}\cdot 5^{10}\cdot 101^{6} \)	$C_2^4.D_4$ (as 16T339)	Trivial (GRH)
16.0.105747725158992197265625.3	x^16 - 5x^15 + 6x^14 + 15x^13 - 51x^12 + 16x^11 + 213x^10 - 47x^9 - 306x^8 + 245x^7 + 469x^6 - 166x^5 - 274x^4 + 175x^3 + 255x^2 + 100x + 25	\( 5^{10}\cdot 101^{8} \)	$C_2^4.D_4$ (as 16T339)	$[4]$ (GRH)
16.0.105747725158992197265625.4	x^16 - 4x^15 + 12x^14 - 12x^13 - 12x^12 + 8x^11 + 253x^10 - 791x^9 + 1455x^8 - 2082x^7 + 2562x^6 - 2006x^5 + 1113x^4 - 264x^3 - 102x^2 + 153x + 71	\( 5^{10}\cdot 101^{8} \)	$C_2^4.D_4$ (as 16T339)	$[2]$ (GRH)
16.0.105747725158992197265625.5	x^16 + 7x^14 - 6x^12 - 47x^10 + 124x^8 + 563x^6 + 1272x^4 + 820x^2 + 121	\( 5^{10}\cdot 101^{8} \)	$C_2^4.D_4$ (as 16T339)	$[2]$ (GRH)
16.0.105747725158992197265625.6	x^16 - 8x^15 + 38x^14 - 126x^13 + 311x^12 - 592x^11 + 978x^10 - 1513x^9 + 2055x^8 - 2222x^7 + 1220x^6 + 689x^5 - 1311x^4 + 460x^3 + 1310x^2 - 1290x + 355	\( 5^{10}\cdot 101^{8} \)	$C_2^4.D_4$ (as 16T339)	$[4]$ (GRH)
16.0.182363546697188582693881.1	x^16 - 3x^15 + 7x^14 - 18x^13 + 32x^12 - 16x^11 + 47x^10 - 64x^9 + 87x^8 - 280x^7 + 618x^6 - 640x^5 + 866x^4 - 623x^3 + 118x^2 + 108x + 16	\( 17^{10}\cdot 67^{6} \)	$C_2^4.D_4$ (as 16T339)	Trivial (GRH)
16.0.182363546697188582693881.2	x^16 - 4x^15 + 9x^14 - 16x^13 + 20x^12 + 8x^11 - 208x^10 + 439x^9 + 175x^8 - 927x^7 - 222x^6 - 197x^5 + 933x^4 + 2070x^3 + 1196x^2 + 224x + 256	\( 17^{10}\cdot 67^{6} \)	$C_2^4.D_4$ (as 16T339)	Trivial (GRH)
16.0.679372896384640000000000.3	x^16 + 7x^14 + 21x^12 + 30x^10 + 35x^8 + 150x^6 + 525x^4 + 875x^2 + 625	\( 2^{16}\cdot 5^{10}\cdot 101^{6} \)	$C_2^4.D_4$ (as 16T339)	$[2]$ (GRH)
16.0.679372896384640000000000.4	x^16 + x^14 + 14x^12 + 20x^10 + 135x^8 + 525x^6 + 975x^4 + 1125x^2 + 625	\( 2^{16}\cdot 5^{10}\cdot 101^{6} \)	$C_2^4.D_4$ (as 16T339)	$[12]$ (GRH)
16.0.679372896384640000000000.5	x^16 - 4x^14 + 4x^12 + 10x^10 + 135x^8 - 675x^6 + 1350x^4 - 1375x^2 + 625	\( 2^{16}\cdot 5^{10}\cdot 101^{6} \)	$C_2^4.D_4$ (as 16T339)	$[2]$ (GRH)
16.0.679372896384640000000000.6	x^16 + 8x^14 + 36x^12 + 115x^10 + 285x^8 + 575x^6 + 900x^4 + 1000x^2 + 625	\( 2^{16}\cdot 5^{10}\cdot 101^{6} \)	$C_2^4.D_4$ (as 16T339)	$[2]$ (GRH)
16.0.679372896384640000000000.7	x^16 + 4x^14 + 4x^12 - 10x^10 + 135x^8 + 675x^6 + 1350x^4 + 1375x^2 + 625	\( 2^{16}\cdot 5^{10}\cdot 101^{6} \)	$C_2^4.D_4$ (as 16T339)	$[8]$ (GRH)
16.0.679372896384640000000000.8	x^16 - x^14 + 14x^12 - 20x^10 + 135x^8 - 525x^6 + 975x^4 - 1125x^2 + 625	\( 2^{16}\cdot 5^{10}\cdot 101^{6} \)	$C_2^4.D_4$ (as 16T339)	$[2]$ (GRH)
16.0.844148415947491674530641.1	x^16 + 10x^14 + 63x^12 + 544x^10 + 2153x^8 + 2808x^6 + 1855x^4 + 714x^2 + 121	\( 13^{6}\cdot 53^{10} \)	$C_2^4.D_4$ (as 16T339)	Trivial (GRH)
16.0.844148415947491674530641.2	x^16 - 8x^15 + 30x^14 - 70x^13 + 135x^12 - 264x^11 + 436x^10 - 475x^9 + 556x^8 - 1134x^7 + 1598x^6 - 1099x^5 + 352x^4 - 102x^3 - 5129x^2 + 5173x + 7039	\( 13^{6}\cdot 53^{10} \)	$C_2^4.D_4$ (as 16T339)	Trivial (GRH)